$f(x)=8x^3+5$ $h(x)=\sqrt[3]{x-5}$ Write $(h\circ f)(x)$ as an expression in terms of $x$. $(h\circ f)(x)=$
Solution: First, let's write $(h\circ f)(x)$ as $h(f(x))$. Next, we write $f(x)$ as the input to function $h$. $h({f(x)})=\sqrt[3]{{f(x)}-5}$ Since $f(x)=8x^3+5$, this becomes: $\begin{aligned} h({f(x)})&=\sqrt[3]{({8x^3+5})-5}\\ \\ &=\sqrt[3]{8x^3}\\ \\ &=2x\\ \\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $(h\circ f)(x)=2x$